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3 years ago

9

The area of a rectangle is 63 m2 , and the length of the rectangle is 5 m more than double the width. find the dimensions of the

rectangle.

1 answer:

Kamila [148]3 years ago

7 0

If you let x represent the width of the rectangle, then you can write the equation for area as
.. x(2x +5) -63 = 0
This has positive solution x=4.5.

The rectangle is 4.5 meters by 14 meters.

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G=x-c/x. for x<br><br>how do yoy make this an equation for x? help

zzz [600]

1.
$\displaystyle \text{if }\quad G=x- \frac{C}{x} \\\\$

$x \neq 0$

Multiply both sides by x:

$\displaystyle Gx=x\bigg(x- \frac{C}{x}\bigg )\\\\Gx=x^2-C$

Subtract from both sides Gx:
$Gx-Gx=x^2-C-Gx\\x^2-Gx-C=0$

Then solve this equation:

$\displaystyle x^2-Gx-C=0\\\\x_{1,2}= \frac{G\pm \sqrt{G^2+4C} }{2}$

2.
$\displaystyle\text{if}\quad G= \frac{x-C}{x}$

$x \neq 0$

Multiply both sides by x:

$Gx=x-C$

Subtract from both sides Gx:

$x-C-Gx=0$

Then solve this equation:

$\displaystyle x-Gx-C=0\\x(1-G)=C\\x= \frac{C}{1-G}$

7 0

3 years ago

1. Find the simple interest on a $3,219.00 principal, deposited for six years at a rate of 1.51%.

Nataliya [291]

Answer:

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

4 0

3 years ago

Can someone check if my answer is correct? Thank you!

a_sh-v [17]

Answer:

Step-by-step explanation:

you are correct.

3 0

3 years ago

Which figure is the image produced by applying the composition T 0,3 o R0,90 to figure R?

Lyrx [107]

We are given original image R.

It is being translated by (0,3) first and then rotated by a positive angle 90 degrees.

Translation by (0,3) represents (x,y) --> (x, y+3) rule.

Positive 90 degree rotation represents, counterclockwise rotation.

The rule for counterclockwise rotation is (x,y) --> (-y,x).

Therefore, final rule for would be

(x,y) --> ( -y,x+3 )

Let us take a coordinate of R on y-axis as (0,-4).

Now if we apply rule (x,y) --> ( -y,x+3 ) we get

(0,-4) --> (-(-4), 0+3) = (4,3).

Let us check the figure with coordinate (4,3).

We can clearly see that Figure H has transformed coordinate (4,3).

<h3>Therefore, correct option is first option A. figure H.</h3>

8 0

3 years ago

The sugar content of the syrup in canned peaches is normally distributed. A random sample of n = 10 cans yields a sample standar

Serggg [28]

Answer:

The 95% confidence interval is given by:

3.30<σ<8.76

Step-by-step explanation:

1) Data given and notation

s=4.798 represent the sample standard deviation

$\bar x$ represent the sample mean

n=10 the sample size

Confidence=95% or 0.95

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=10-1=9$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical values.

The excel commands would be: "=CHISQ.INV(0.025,9)" "=CHISQ.INV(0.975,9)". so for this case the critical values are:

$\chi^2_{\alpha/2}=19.022$

$\chi^2_{1- \alpha/2}=2.700$

And replacing into the formula for the interval we got:

$\frac{(9)(4.798)^2}{19.022} \leq \sigma \frac{(9)(4.798)^2}{2.700}$

$10.892 \leq \sigma^2 \leq 76.736$

Now we just take square root on both sides of the interval and we got:

$3.30 \leq \sigma \leq 8.76$

So the best option would be:

3.30<σ<8.76

7 0

3 years ago